Problem: Solve for $x$ and $y$ using elimination. ${-3x+5y = 31}$ ${3x+6y = 57}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $11y = 88$ $\dfrac{11y}{{11}} = \dfrac{88}{{11}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-3x+5y = 31}\thinspace$ to find $x$ ${-3x + 5}{(8)}{= 31}$ $-3x+40 = 31$ $-3x+40{-40} = 31{-40}$ $-3x = -9$ $\dfrac{-3x}{{-3}} = \dfrac{-9}{{-3}}$ ${x = 3}$ You can also plug ${y = 8}$ into $\thinspace {3x+6y = 57}\thinspace$ and get the same answer for $x$ : ${3x + 6}{(8)}{= 57}$ ${x = 3}$